Related papers: A model-free Screening procedure
Herein, we propose a Spearman rank correlation based screening procedure for ultrahigh-dimensional data with censored response case. The proposed method is model-free without specifying any regression forms of predictors or response…
This paper explores the following question: what kind of statistical guarantees can be given when doing variable selection in high-dimensional models? In particular, we look at the error rates and power of some multi-stage regression…
We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…
In high-dimensional settings, sparse structures are critical for efficiency in term of memory and computation complexity. For a linear system, to find the sparsest solution provided with an over-complete dictionary of features directly is…
We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference…
For many classification and regression problems, a large number of features are available for possible use - this is typical of DNA microarray data on gene expression, for example. Often, for computational or other reasons, only a small…
Bayesian model selection with improper priors is not well-defined because of the dependence of the marginal likelihood on the arbitrary scaling constants of the within-model prior densities. We show how this problem can be evaded by…
We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection…
We describe a novel procedure for deciding when a mass-action model is incompatible with observed steady-state data that does not require any parameter estimation. Thus, we avoid the difficulties of nonlinear optimization typically…
This article considers ultrahigh-dimensional forecasting problems with survival response variables. We propose a two-step model averaging procedure for improving the forecasting accuracy of the true conditional mean of a survival response…
We develop a Bayesian variable selection method, called SVEN, based on a hierarchical Gaussian linear model with priors placed on the regression coefficients as well as on the model space. Sparsity is achieved by using degenerate spike…
In problems such as variable selection and graph estimation, models are characterized by Boolean logical structure such as presence or absence of a variable or an edge. Consequently, false positive error or false negative error can be…
Let X; Z be r and s-dimensional covariates, respectively, used to model the response variable Y as Y = m(X;Z) + \sigma(X;Z)\epsilon. We develop an ANOVA-type test for the null hypothesis that Z has no influence on the regression function,…
Two popular variable screening methods under the ultra-high dimensional setting with the desirable sure screening property are the sure independence screening (SIS) and the forward regression (FR). Both are classical variable screening…
High-dimensional tests are applied to find relevant sets of variables and relevant models. If variables are selected by analyzing the sums of products matrices and a corresponding mean-value test is performed, there is the danger that the…
The varying-coefficient model is an important nonparametric statistical model that allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is big, the issue of variable selection…
Let X be a d dimensional vector of covariates and Y be the response variable. Under the nonparametric model Y = m(X) + {\sigma}(X) \in we develop an ANOVA-type test for the null hypothesis that a particular coordinate of X has no influence…
We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. We assume that this set is selected via a very simple approach that is commonly used across scientific disciplines:…
We introduce a generic estimator for the false discovery rate of any model selection procedure, in common statistical modeling settings including the Gaussian linear model, Gaussian graphical model, and model-X setting. We prove that our…
Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression…